Triangles
posted by Anonymous .
Right traingles C and D share a leg. If the ratio of the area of traingle C to the area of traingle D is 5:9, C’s hypotenuse is of length 25, and D’s hypotenuse is of length 39, what is the area of C?

Triangles 
Reiny
For the nonshared legs,
let the shorter be x and the longer be y
let the length of the shared leg be h
so x^2 + h^2 = 25^2 and y^2 + h^2 = 39^2
h^2 = 625x^2 and h^2 = 1521  y^2
625  x^2 = 1521  y^2
y^2  x^2 = 896
Also, (1/2)xh /(1/2)yh = 5/9
x/y = 5/9
9x = 5y
x = 5y/9
y^2  25y^2/81 = 896
times 81
81y^2  25y^2 = 72576
56y^2 = 72576
y^2 = 1296
y = ± 36 , rejecting the negative, since we can't have a negative length of a line
y= 36, then in x=5y/9 >
take it from here
Respond to this Question
Similar Questions

geometry
a right traingle has legs of lengths 3 centimeters and 5 centimeters. Use the pythagorean theorem to find the area of a square drwan on the hypotenuse of the triangle. 
math/geometry
complete the statements: To find the length of the hypotenuse of a 454590 triangle, multiply the length of one of the legs by:? 
math
I have 14 questions and I was wondering if someone could check my answers. This is a do or die situation. If I don't get an A, I may not get to graduate. I really appreciate you taking your time to double check theses for me. Thanks … 
math
5. Find the length of the hypotenuse of a right triangle with legs of 20 cm and 21 cm. 41 cm 841 cm 6 cm 29 cm 6. The length of the hypotenuse of a right triangle is 15 cm. The length of one leg is 9 cm. Find the length of the other … 
Math Algebra
The length of the hypotenuse of a right triangle is 30 m. The length of one leg is 20 cm. Find the length of the other leg. Round your answer to the nearest tenth I know how to do hypotenuse but this doesn't seem to work out...help … 
MATH MS.SUE HELP PLEASE!
Could somebody help me I don't understand any of this. Could someone show me or tell me how to work the problems? 
Math
1) The hypotenuse of an isosceles right triangle is 8 cm longer than either of its legs. Note that an isosceles right triangle is a right triangle whose legs are the same length. Find the exact length of its legs and its hypotenuse. … 
Geometry
I need help in this problem: A 14foot ladder is leaning against a house so that its top touches the top of the wall. the bottom of the ladder is 8 feet away from the wall. which of these can be used to find the height of the wall? 
math
find the area of right traingle of base 1.2m and hypotenuse 3.7. 
Math
Jeremy loves right triangles that have side length 1. In fact, he loves to combine them so that the hypotenuse of one becomes the leg of the next. If the longer leg of the first triangle is sqrt 11, what will be the hypotenuse of the …