QN07: The altitude of a right Ais 7cm less than its base. If the hypotenuse is 13cm. find the other two sides (7cm)​

Question

QN07: The altitude of a right Ais 7cm less than its base. If the hypotenuse is 13cm.
find the other two sides (7cm)​

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Eloise 21 hours 2021-10-13T08:57:31+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-13T08:59:21+00:00

    Solution

    Let the base of right triangle be x the altitude be (x – 7)

    Hypotenuse = 13 cm

    (hypotenuse)²=(base)²+(perpendicular)²

    (13)² = (x)² + (x – 7)²

    169 = x² + x² + (7)² – 2 × x × 7

    169 = 2x² + 49 – 14x

    169 – 49 = 2x² – 14x

    120 = 2x² – 14x

    2x² – 14x – 120 = 0

    2(x² – 7x – 60) = 0

    x² – 7x – 60 = 0

    x² + 7x – 12x – 60x = 0

    x(x + 7) – 12(x + 7) = 0

    (x + 7)(x – 12) = 0

    ______________

    (x + 7) = 0

    x = – 7

    ____________

    (x – 12) = 0

    x = 12

    ______________

    Base = x = 12 m

    Altitude = (x – 7) = (12 – 7) = 5m

    0
    2021-10-13T08:59:25+00:00

    Given

    The altitude of a right is 7cm less than its base. If the hypotenuse is 13cm.

    Find out

    Find the other two sides

    Solution

    Let the base of right triangle be x the altitude be (x 7)

    • Hypotenuse = 13 cm

    According to the Pythagoras theorem

    (hypotenuse)²=(base)²+(perpendicular)²

    ➟ (13)² = (x)² + (x – 7)²

    Apply identity :

    (a b)² = + 2ab

    ➟ 169 = x² + x² + (7)² – 2 × x × 7

    ➟ 169 = 2x² + 49 – 14x

    ➟ 169 – 49 = 2x² – 14x

    ➟ 120 = 2x² – 14x

    ➟ 2x² – 14x – 120 = 0

    ➟ 2(x² – 7x – 60) = 0

    ➟ x² – 7x – 60 = 0

    Splitting middle term

    x² + 7x – 12x – 60x = 0

    ➟ x(x + 7) – 12(x + 7) = 0

    ➟ (x + 7)(x – 12) = 0

    Either

    ➟ (x + 7) = 0

    ➟ x = – 7

    Or

    ➟ (x – 12) = 0

    ➟ x = 12

    Length can’t be in negative

    Hence,

    • Base = x = 12 m
    • Altitude = (x – 7) = (12 – 7) = 5m

    \rule{200}3

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