#### Question

In Figure, DE || BC If DE = 4cm, BC = 8 cm and Area (ΔADE) = 25 cm2, find the area of ΔABC.

#### Solution

We have, DE || BC, DE = 4 cm, BC = 8 cm and area (ΔADE) = 25cm^{2}

In ΔADE and ΔABC

∠A = ∠A [Common]

∠ADE = ∠ABC [Corresponding angles]

Then, ΔADE ~ ΔABC [By AA similarity]

By area of similar triangle theorem

`("Area"(triangleADE))/("Area"(triangleABC))="DE"^2/"BC"^2`

`rArr25/("Area"(triangleABC))=4^2/8^2`

⇒ Area (ΔABC) = `(25xx64)/16=100"cm"^2`

Is there an error in this question or solution?

#### APPEARS IN

Solution In Figure, De || Bc If De = 4cm, Bc = 8 Cm and Area (δAde) = 25 Cm2, Find the Area of δAbc. Concept: Areas of Similar Triangles.