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  • Write True or False and justify your answer: The area of the isosceles triangle is frac{5}{4} sqrt{11}cm^{2}, if the perimeter is 11 cm and the base is 5 cm.

Write True or False and justify your answer:

The area of the isosceles triangle is \frac{5}{4}\sqrt{11}cm^{2}, if the perimeter is 11 cm and the base is 5 cm.

Answers (1)

[True]

Given

Area\; of\; isosceles\; triangle= \frac{5}{4}\sqrt{11}cm^{2}

Perimeter\; of\; triangle= 11cm

We know that

Perimeter= x+x+5 \; \; \; \; \; \; \; \; \; \; \left [ \therefore Let\; equal\; sides\; of\; triangle= x \right ]

 11cm-5cm= 2x

\Rightarrow 6cm= 2x\Rightarrow x= \frac{6}{2}cm

\Rightarrow x=3cm

Now, in right triangle ADB

Using Pythagoras theorem

\left ( AB \right )^{2}=\left ( AD \right )^{2}+\left ( BD \right )^{2}

\left ( 3 \right )^{2}=\left ( AD \right )^{2}+\left ( \frac{5}{2} \right )^{2}

9-\frac{25}{4}=\left ( AD \right )^{2}

\Rightarrow AD= \sqrt{9-\frac{25}{4}}

\Rightarrow AD= \sqrt{\frac{36-25}{4}}

AD= \sqrt{\frac{11}{4}}=\frac{\sqrt{11}}{2}CM\; \; \; \; \; \; \; \left [ Q\sqrt{4} =\sqrt{2\times 2}=2\right ]

Area\; of\; isosceles\; triangle=\frac{1}{2}\times base\times height

= \frac{1}{2}\times 5\times\frac{\sqrt{11}}{2}=\frac{5\sqrt{11}}{4}cm^{2}

Therefore the given statement is true.

Posted by

infoexpert21

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