Question

The three sides of a right-angled triangle are x, x+1 and 5. write down the value of x and the area, if the longest side is 5.

Answer 1

here
by pythagoreas theorem
${(x + 1)}^{2} + {x}^{2} = {5}^{2}$
opening
${(x + 1)}^{2} = {x}^{2} + 1 + 2x$
therefore
${x}^{2} + 1 + 2x + {x}^{2} = 25$
$2 {x}^{2} + 2x = 24$
$2( {x}^{2} + x) = 24$
${x}^{2} + x = 12$
${x}^{2} + x - 12 = 0$
${x}^{2} + 4x - 3x - 12 = 0$
$x(x + 4) - 3(x + 4) = 0$
$(x - 3)(x + 4) = 0$
either x=3 or x=-4
but side cannot be negative therefore x=3
hence, other side =4
Area=1/2×4×3
=2×3
=
$6 {cm}^{2}$
hence area =6sq cm

Answer 2

Step-by-step explanation:

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