Question

How many square inches larger is the area ABC then CDE shown in figure

Answer 1

D

Explanation:

the area (A) of Δ CDE is calculated as

A =
`(1)/(2)` bh ( b is the base and h the perpendicular height )

here b = 8 and h = 6 , then

A =
`(1)/(2)` × 8 × 6 = 4 × 6 = 24 cm²

Δ CDE and Δ ABCare similar ( AA postulate )

given the scale factor of 2 similar figures is k

then the factor of their areas is k²

here the scale factor k of the 2 triangles is the ratio of corresponding sides , Δ CBA to Δ CDE , then

k =
`(AB)/(CD)` =
`(12)/(8)` = 1.5

then the ratio of their area is 1.5² = 2.25

that is area of Δ ABC is 2.25 times area of Δ CDE

area o Δ ABC = 2.25 × 24 cm² = 54 cm²

then 54 cm² - 24 cm² = 30 cm²

Thus

area of Δ ABC is 30 cm² greater than Δ CDE