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Heron’s Formula — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsHeron’s Formula1 Mark
Question
Write the correct answer in the following:
An isosceles right triangle has area 8cm2. The length of its hypotenuse is:
  1. $\sqrt{32}\text{cm}$
  2. $\sqrt{16}\text{cm}$
  3. $\sqrt{48}\text{cm}$
  4. $\sqrt{24}\text{cm}$
✓

Answer

  1. $\sqrt{32}\text{cm}$

Solution:

ABC is an isosceles right triangle. We have,

$\text{AB}=\text{BC}=\text{a cm}$

Area of $\triangle=\frac{1}{2}\text{base}\times\text{Height}$

$\Rightarrow\ 8=\frac{1}{2}\times\text{a}\times\text{a}$ $\big[\because\ \text{AB}=\text{BC}=\text{a cm}\big]$

$\Rightarrow\ \text{a}^2=16$ $\therefore\ \text{a}=+\sqrt{16}=4\text{cm}$

Using Pythagoras theorem,

Hypotenuse $\text{AC}=\sqrt{4^2+4^2}$

$=\sqrt{16+16}=\sqrt{32}\text{cm}$

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