BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

The quadrilateral ABCD is a kite. If AB = BC = 20, CD = DA =

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

The quadrilateral ABCD is a kite. If AB = BC = 20, CD = DA =

by Max@Math Revolution » Mon Jun 10, 2019 11:23 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

[GMAT math practice question]

The quadrilateral ABCD is a kite. If AB = BC = 20, CD = DA = 15 and BD = 7, what is the area of the kite ABCD shown in the figure below?

Image

A. 60
B. 72
C. 84
D. 96
E. 108
Top
Source: — Problem Solving |
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

by Max@Math Revolution » Wed Jun 12, 2019 6:11 pm
=>

Image

Let x and y be the lengths of DE and CE, repectively.
From the right triangle CDE, we have CD^2 = x^2 + y^2 or x^2+y^2=225.
From the right triangle BCD, we have BC^2 = (x+7)^2 + y^2 or (x+7)^2 + y^2 = 400.
Subtracting the first equation from the second yields (x+7)^2 - x^2 = (x+7+x)(x+7-x) = 7(2x+7) = 175, and x = 9.
y = 12 since y^2 = 225 - x^2 = 225 - 81 = 144.
The area of the kite ABCD is the area of triangle ABC - the area of triangle ADC = (1/2)(2y)(x + 7) - (1/2)(2y)x = (1/2)(24)(16) - (1/2)(24)(9) = (1/2)(24)(16-9) = 12*7 = 84.

Therefore, the answer is C.
Answer: C
Top
Post new topic Post Reply
• Page 1 of 1