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The base of an isoceles of …

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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, 11 months ago

CBSE > Class 09 > Mathematics

2 answers

Sia ? 5 years, 11 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.

Manoj Kumar 5 years, 11 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

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This content has been hidden. One or more users have flagged this content as inappropriate. Once content is flagged, it is hidden from users and is reviewed by myCBSEguide team against our Community Guidelines. If content is found in violation, the user posting this content will be banned for 30 days from using Homework help section. Suspended users will receive error while adding question or answer. Question comments have also been disabled. Read community guidelines at https://mycbseguide.com/community-guidelines.html

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