# Geometry

Find area of a triangle with side lengths 15 15 and 8

1. 👍 0
2. 👎 0
3. 👁 62
1. simplest way:
Heron's Formula
A = √(s(s-a)(s-b)(s-c)), where s = (1/2)the perimeter.

s = (1/2)(15 + 15 + 8) = 19
s-a = 19-15 = 4
s-b = 19-15 = 4
s-c = 19-8 - 11
area = √(19(4)(4)(11) = √3344
= appr 57.83

2nd way: works in this case because it is isosceles.
Sketch the triangle, let the angle between the two equal sides be 2θ
Draw a perpendicular from that angle to the base.
sinθ = 4/15
θ = 15.466..
2θ = 30.932..

area = (1/2)(15)(15)sin30.932..
= 57.83 , same as above

There are other ways, but these two work nicely. The 2nd way of course only worked so fine, because we had an isosceles triangle

1. 👍 0
2. 👎 0
posted by Reiny
2. Thank you!

1. 👍 0
2. 👎 0
3. An easier way would be to find the perpendicular and use pythag. Thm

c^2 = a^2 + b^2
15^2 = 4^2 + b^2
b = 14.45

A = 1/2 bh
A= 1/2 8 x 14.45

you will get the same answer as above.

Depending on the level you are working at this might be what your teacher is looking for.

1. 👍 0
2. 👎 0
posted by John

## Similar Questions

1. ### maths

1.how many non congruent right triangles with positive integer leg lengths have areas that are numerically equal to 3 times their perimeters? 2.a triangle with side lengths in the ratio 3:4:5 is inscribed in a circle of radius

asked by ramesh reddy on May 7, 2013
2. ### Math

If all of the following triangles have the same perimeter, which has the greater area? a) a right triangle with legs of equal lengths b) an equilateral triangle, c) An obtuse triangle d) a triangle whose sides are all different

asked by Anonymous on August 8, 2012
3. ### geometry

i need to figure out side lengths of congruent right isosceles triangle with no lengths given. I know that the hypotenese is 1 per pythogoras constant and the area is a^2/2. I don't have to prove area just side lengths.

asked by carolyn on May 21, 2015
4. ### Trig

The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. (a) Find the area of triangle PQR. (b) Find the length of the projection of segment PQ onto segment PR. (c) Find the

asked by Sarah on April 17, 2010
5. ### math

an isosceles triangle has perimeter of 15m. Find all integral possibilities for the lengths of the side in meters. Hint: the sum of the lengths of any two sides of a triangle must exceed the third side.

asked by emily on October 17, 2018
6. ### geometry/math pls help

The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. (1) Find the sizes of the other two angles of triangle PQR. (2) Find the length of the median drawn to side PQ. (3)

asked by Maryann on April 21, 2010
7. ### math pls

The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. (d) Find the sizes of the other two angles of triangle PQR. (e) Find the length of the median drawn to side PQ. (f)

asked by Maryann on April 21, 2010
8. ### Math (Geometry)

Find the length of the third side of a triangle if the area of the triangle is 18 and two of its sides have lengths of 5 and 10.

asked by Joy on September 20, 2013
9. ### Math Help!

The radius of this circle is one unit. Find the exact lengths of the legs in the right triangle if: Sides a is twice as long as side b. And Sides b is twice as long as side a. Basically the hypotenuse of this triangle is 1 and we

asked by David on December 12, 2015
10. ### Math Help Please

The radius of this circle is one unit. Find the exact lengths of the legs in the right triangle if: Sides a is twice as long as side b. And Sides b is twice as long as side a. Basically the hypotenuse of this triangle is 1 and we

asked by David on December 12, 2015
11. ### Math

The radius of this circle is one unit. Find the exact lengths of the legs in the right triangle if: Sides a is twice as long as side b. And Sides b is twice as long as side a. Basically the hypotenuse of this triangle is 1 and we

asked by David D. on December 12, 2015

More Similar Questions