Question

5) A parallelogram with a base 13 cm has an area 65 cm. The altitude corresponding to the base is a) 12 cm b) 5 cm c) 10 cm d) 20 cm​

Answer 1

Aиѕωєr —

❝ The altitude corresponding to the base is 5 cm ❞

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Giνєи —

• Base of a parallelogram = 13 cm
• Area of parallelogram = 65 cm

Tσ Fiиd —

• Altitude corresponding to the base

Sσℓυтiσи –

✪ If we join one of the diagonal of a parallelogram , then we get 2 equal triangles of equal area .

✪ As we know that are of triangle is :

$\qquad{\pmb{\boxed{\bf{Area_{(triangle)}=\dfrac{1}{2}\times B \times H }}}}$

✪ Here ,

ㅤㅤㅤ➻ B = 13 cm

ㅤㅤㅤ➻ Area = $\sf{\dfrac{65}{2}}$ cm²

ㅤㅤㅤ➻ H = ?

Tнєrєfσrє —

$\qquad\sf{\longrightarrow Area = \dfrac{1}{2}\times Base \times Altitude }$

$\qquad\sf{\longrightarrow \dfrac{65}{2}=\dfrac{1}{2}\times 13\times Altitude }$

$\qquad\sf{\longrightarrow Altitude = \dfrac{65}{2}\times \dfrac{1}{2}\times \dfrac{1}{13}}$

$\qquad\sf{\longrightarrow Altitude=\cancel{\dfrac{130}{26}}}$

$\qquad\sf{\longrightarrow Altitude = 5 }$

$\qquad{\pmb{\sf{\longrightarrow Altitude=5cm}}}$

❝ Hence the altitude of parallelogram corresponding to the base is 5 cm ❞

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