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प्रश्न
The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.
उत्तर
Area of a triangle = `("Height" xx "Base")/2`
Here, Height and base are x and (x + 10 ) and the area is 600
Hence , `x xx (x + 10) xx 1/2 = 600`
⇒ x2 + 10x= 1200
⇒ x2 + 10 x - 1200 = 0
⇒ x2 + 40x - 30 x - 1200 = 0
⇒ x (x + 40} - 30(x + 40) = 0
⇒ (x + 40)(x - 30) = 0, hence x = 30 .
Base = 30+ 10 = 40 cms.
Hence h2= 402 + 302 = 2500
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