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प्रश्न
The length of the sides forming a right angle in a triangle are 5x cm and (3x-1) cm. If the area of the triangle is 60cm2, find the hypotenuse.
उत्तर
Area of a triangle = `("Height" xx "Base")/2`
Here, Height and base are 5x and (3x-1) and the area is 60
Hence , `5x xx (3x - 1) xx 1/2 = 60`
⇒ 15x2 - 5x = 120
⇒ 3x2 - x -24 = 0
⇒ 3x2 - 9x + 8x - 24 = 0
⇒3x (x - 3) +8(x - 3) = 0
⇒ (3x + 8)(x - 3) = 0, hence x = 3.
Sides are 5 x 3 and 3 x 3-1= 15 and 8 ems.
⇒ Hence, h2= 152 + 82 = 289
Hypotenuse = 17 cms.
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