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The base of an isoceles of triangle measure 24cm area of triangle 192cm square. Find the perimeter

Posted by Ash J 5 years, 8 months ago

CBSE > Class 09 > Mathematics

2 answers

Sia ? 5 years, 8 months ago

Here, base, b = 24 cm, and let each equal side be a cm. Then,
area = $\frac { 1 } { 4 } b \sqrt { 4 a ^ { 2 } - b ^ { 2 } } \text { sq units } = \frac { 1 } { 4 } \times 24 \times \sqrt { 4 a ^ { 2 } - 576 } \mathrm { cm } ^ { 2 }$
= $12 \times \sqrt { a ^ { 2 } - 144 } \mathrm { cm } ^ { 2 }$
But, area = 192 cm² [given].
$\therefore \quad 12 \times \sqrt { a ^ { 2 } - 144 } = 192 \Rightarrow \sqrt { a ^ { 2 } - 144 } = 16$
$\Rightarrow a ^ { 2 } - 144 = 256 \Rightarrow a ^ { 2 } = 400 \Rightarrow a = 20$
$\therefore\quad$ perimeter of the triangle = (2a + b) cm
= (2 $\times$ 20 + 24) cm = 64 cm.

1Thank You

Manoj Kumar 5 years, 8 months ago

24cm one side and anotjer two are equal and will be x 192=1/2(base)(hight) 192=1/2×24(x) 192=12X 192/12=x 16=x So, two equal sides are of 16cm. Perimeter =24+16+16 P=54

1Thank You

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