Δ ABC is similar to Δ DEF. The area of Δ ABC is 100cm² and the area of Δ DEF is 49 cm². If the altitude of Δ ABC = 5 cm, then the corresponding altitude of Δ DEF is:

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Question

This question was previously asked in

MP Police Constable 2023 Official Paper (Held On: 10 Sept, 2023 Shift 2)

Answer 1

Given:

ΔABC is similar to ΔDEF

Area of ΔABC = 100 cm²

Area of ΔDEF = 49 cm²

Altitude of ΔABC = 5 cm

Formula used:

If two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides or altitudes:

Area of ΔABC / Area of ΔDEF = (Altitude of ΔABC / Altitude of ΔDEF)²

Calculation:

\(\dfrac{\text{Area of ΔABC}}{\text{Area of ΔDEF}} = \left(\dfrac{\text{Altitude of ΔABC}}{\text{Altitude of ΔDEF}}\right)^2\)

⇒ \(\dfrac{100}{49} = \left(\dfrac{5}{\text{Altitude of ΔDEF}}\right)^2\)

⇒ \(\sqrt{\dfrac{100}{49}} = \dfrac{5}{\text{Altitude of ΔDEF}}\)

⇒ \(\dfrac{10}{7} = \dfrac{5}{\text{Altitude of ΔDEF}} \)

⇒ \(\text{Altitude of ΔDEF} = \dfrac{5 \times 7}{10} \)

⇒ \(\text{Altitude of ΔDEF} = 3.5 \, \text{cm}\)

∴ The correct answer is option (4).

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