Question

Use the diagram to determine which statement is true

A) Area(ABCD) - AREA(DGA) = AREA(DEFG)

B) Area(ABCD) - AREA(GHIA) = AREA(DGA)

C) Area(ABCD) + AREA(DGA) = AREA(GHIA)

D) Area(DEFG) + AREA(GHIA) = AREA(ABCD)

Answer 1

D)

Explanation:

The DGA triangle is the right triangle.

We have three squares built on the sides of a given triangle.

Based on Pythagoras' theorem we have:

Answer 2

A. Area of ABCD - Area of DGA = Area of DEFG
s^2 - 1/2bh = s^2
(5)^2 - 1/2(4)(3) = (3)^2
25 - 1/2(12) = 9
25 - 24 = 9
1 not equal to 9

B. Area of ABCD - Area of GHIA = Area of DGA
s^2 - s^2 = 1/2bh
(5)^2 - (4)^2 = 1/2(4)(3)
25 - 16 = 1/2(12)
9 not equal to 6

C. Area of ABCD + Area of DGA = Area of GHIA
s^2 + 1/2bh = s^2
(5)^2 + 1/2(4)(3) = (4)^2
25 + 1/2(12) = 16
25 + 6 = 16
31 not equal to 16

D. Area of DEFG + Area of GHIA = Area of ABCD
s^2 + s^2 = s^2
(3)^2 + (4)^2 = (5)^2
9 + 16 = 25
25 = 25

The answer is D.