# Geometry

In quadrilateral ABCD, we have AB = BC = CD = DA, AC = 14, and BD = 48. Find the perimeter of ABCD.

1. 👍 0
2. 👎 0
3. 👁 258
1. A quadrilateral with all four sides equal is a rhombus, whose area is half the product of the diagonals AC and BD.

1. 👍 0
2. 👎 0
posted by MathMate
2. Yeah, but we're not trying to find the area?

1. 👍 0
2. 👎 0
3. Sorry.
In that case, we make use of the fact that rhombuses have diagonals which intersect at right-angles.
Thus each side is the hypotenuse of a right triangle with legs equal to the half-diagonals.

Thus if s=length of each side of the rhombus, then
s²=(AC/2)²+(BD/2)²
using Pythagoras theorem.
Calculate
s=√(7²+24²)
=25

The perimeter is 4s.

1. 👍 0
2. 👎 0
posted by MathMate
4. Stop cheating Sheenybeany!

1. 👍 0
2. 👎 1
posted by AoPS

## Similar Questions

1. ### Geometry

Quadrilateral ABCD is a parallelogram. If adjacent angles are congruent, which statement must be true? A. Quadrilateral ABCD is a square. B. Quadrilateral ABCD is a rhombus. C. Quadrilateral ABCD is a rectangle. D. Quadrilateral

asked by Lauren on July 5, 2017
2. ### geometry

Heather is given the coordinates of the vertices of quadrilateral ABCD. ABCD. She is asked to prove whether the quadrilateral is a parallelogram. Her proof follows the diagram. Given: Quadrilateral ABCD ABCD has vertices at

asked by dee on March 4, 2020
3. ### math

(a) Construct a quadrilateral ABCD in which AB = 10cm , angle ABC = 120° , angle BAD = 60°, BC =7cm and AD = 11cm. (b) Measure and write the length of CD. (c) Within the quadrilateral ABCD draw the locus of points which are (i)

asked by Winfridah on March 14, 2020
4. ### maths

Given is a quadrilateral ABCD,diagonals AC and BDare such that AO=BO=CO=DO=3cm,where Ois point of intersection of AC and BD then quadrilateral ABCD is a rectangle State true or false with reason

asked by faizel on January 6, 2013

ABCD is a quadrilateral with angle ABC a right angle. The point D lies on the perpendicular bisector of AB. The coordinates of A and B are (7, 2) and (2, 5) respectively. The equation of line AD is y = 4x − 26. find the area of

asked by ALEX on December 22, 2016
1. ### geometry

quadrilateral ABCD has right angles at B and D. If ABCD is kite-shaped with AB=AD=20 and BC=CD=15, find the radius of the circle inscribed in ABCD.

asked by Hanna on December 4, 2011
2. ### algbra

a parallelogram is a quadrilateral whose opposite sides are parallel. The vertices of the quadrilateral ABCD are A(2,0), B(-2,2),C(2,8), D(6,6). Determine whether or not ABCD is a Parallel.

asked by asfasfas on January 18, 2011
3. ### Geometry

Graph the following quadrilateral: A(-2,-3) B(-1,1) C(4,-1) D(3,-5) Graph quadrilateral ABCD after a translation which moves point D to the origin. Label the new quadrilateral A' B' C' D'.

asked by iceberg on January 6, 2015
4. ### math

In a quadrilateral ABCD, AB || DC and AD||BC . Find the perimeter of ΔCOD if the diagonals of the quadrilateral intersect each other at pointOand AC = 20 in, BD = 20 in, AB = 13 in.

asked by Anonymous on March 19, 2017
5. ### geometry

What is the most precise name for quadrilateral ABCD with vertices A(–3, 2), B(–1, 4), C(4, 4), and D(2, 2)? 1. parallelogram 2. rhombus 3. quadrilateral 4. rectangle

asked by Bob on January 11, 2013
6. ### math

write a sequence of the transformation that maps quadrilateral ABCD onto quadrilateral A"B"C"D" in picture below.

asked by cmac on February 19, 2017

More Similar Questions