in right triangle abc the ratio of the lengths of the two legs (non-hypotenuse sides) is 2 to 5. if the area of triangle abc is 20 what is the length of the hypotenuse?
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Let the common multiple be x
area of triangle =1/2×base×height
20=1/2×2x×5x
20×2=10x^2
40=10x^2
40/10=x^2
4=x^2
2=x
x=2
the sides are 2x=2×2=4 and 5x=5×2=10
Pythagoras theorem
(Hypotaneouse)^2=(side1)^2+(side2)^2
(hypo)^2=4^2+(10)^2
(hypo)^2=16+100
(hypo)^2=116
hypo=✓4×29....taking square root on both the side
hypo=2✓29
area of triangle =1/2×base×height
20=1/2×2x×5x
20×2=10x^2
40=10x^2
40/10=x^2
4=x^2
2=x
x=2
the sides are 2x=2×2=4 and 5x=5×2=10
Pythagoras theorem
(Hypotaneouse)^2=(side1)^2+(side2)^2
(hypo)^2=4^2+(10)^2
(hypo)^2=16+100
(hypo)^2=116
hypo=✓4×29....taking square root on both the side
hypo=2✓29
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Answer:
50 is the ans
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