Question

7. If the base of a right angled triangle is 8 cm and the hypotenuse is 17 cm, find
area.
its
​

Answer 1

Appropriate Question:

• If the base of a right angled triangle is 8 cm and the hypotenuse is 17 cm, find its area.

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

⠀

⋆ DIAGRAM :

$\setlength{\unitlength}{1.5cm}\begin{picture}(6,2)\linethickness{0.5mm}\put(7.7,2.9){\large\sf{A}}\put(7.7,1){\large\sf{B}}\put(10.6,1){\large\sf{C}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\qbezier(10.5,1)(10,1.4)(8,2.9)\put(7.1,2){\sf{\large{?cm}}}\put(9,0.7){\sf{\large{8cm}}}\put(9.4,1.9){\sf{\large{17 cm}}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\end{picture}$

⠀

$\underline{\bigstar\:\boldsymbol{By\: Using\; Pythagoras\: Theorem :}}$

⠀⠀⠀⠀

$:\implies\sf (AB)^2 + (BC)^2 = (AC)^2 \\\\\\:\implies\sf (AB)^2 = (AC)^2 - (BC)^2 \\\\\\:\implies\sf (AB)^2 = (17)^2 - (8)^2 \\\\\\:\implies\sf (AB)^2 = 289 - 64 \\\\\\:\implies\sf AB^2 = 225 \\\\\\:\implies\sf AB = \sqrt{225} \\\\\\:\implies{\underline{\boxed{\sf{AB = 15\;cm}}}}$

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

◗ To find out the Area of a right angle triangle formula is given by :

⠀⠀

$\star\;\boxed{\sf{\pink{Area_{\:(triangle)} = \dfrac{1}{2} \times Base \times Height}}}$

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{Putting\;values\: :}}$⠀⠀

⠀⠀⠀⠀

$:\implies\sf Area_{\;(triangle)} = \dfrac{1}{\cancel{\;2}} \times \: \cancel{\;8} \; \times 15 \\\\\\:\implies\sf Area_{\;(triangle)} = 4 \times 15 \\\\\\:\implies{\underline{\boxed{\frak{\pink{Area_{\:(triangle)} = 60\;cm^2}}}}}\;\bigstar$

⠀⠀⠀⠀

$\therefore{\underline{\sf{Hence,\;area\;of\;right\;angle\; \triangle\;is\;\bf{ 60\;cm^2}.}}}$

Answer 2

Answer:

Given :

• The base of a right angled triangle is 8 cm and the hypotenuse is 17 cm.

Find Out :

• Area.

Solution :

By Pythagoras Theorem we get,

➻ (AC)² = (AB)² + (BC)²

➻ (17)² = (8)² + (BC)²

➻ 289 = 64 + (BC)²

➻ 289 - 64 = (BC)²

➻ 225 = (BC)²

➻ √225 = BC

➻ 15 cm = BC

Area of triangle = $\dfrac{1}{2}$ × BC × AB

➻ Area of triangle = $\dfrac{1}{2}$ × 15 × 8

➻ Area of triangle = 60 cm².

∴ The area of triangle is 60 cm².