Question

If A ABC A PQR and ar (ABC) = 81 cm", ar (APQR) = 121 cm² and altitude AD = 9 cm. Find the
altitude PM
​

Answer 1

Answer:

given

(ABC)= 81

(APQR) =121

AD=9

PM=11

Answer 2

The length of the altitude PM is 11 cm.

Explanation:

Given : ΔABC ≈ Δ PQR

ar (ABC) = 81 cm²

ar (PQR) = 121 cm²

Length of altitude AD = 9 cm

To find : altitude PM

​

If two triangles are similar then the ratio of the area of the triangles is equal to the ratio of the square of the corresponding altitudes.

$\dfrac{\text{ar (ABC)}}{ar(PQR)}=\dfrac{(AD)^2}{(PM)^2}$

$\dfrac{81}{121}=\dfrac{9^2}{PM^2}\\\\ \dfrac{81}{121}=\dfrac{81}{PM^2}\\\\PM^2=121\\\\ PM=\sqrt{121}=11$

Hence, the length of the altitude PM is 11 cm.

# Learn more :

If triangle ABC is similar to the triangle QRP, ar(ABC)/ar(PQR)= 9/4, AB=18 cm BC=15 cm, then PR= ?

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