Advertisements
Advertisements
Question
Area of a right-angled triangle is 30 cm2. If its smallest side is 5 cm, then its hypotenuse is ______.
Options
14 cm
13 cm
12 cm
11 cm
Advertisements
Solution
Area of a right-angled triangle is 30 cm2. If its smallest side is 5 cm, then its hypotenuse is 13 cm.
Explanation:
Given, area of a right-angled triangle = 30 cm2
And smallest side i.e. base = 5 cm
We know that,
Area of right angled triangle = `1/2` × Base × Height
∴ 30 = `1/2` × 5 × Height
⇒ Height = `(30 xx 2)/5`
⇒ Height = 12 cm
Now, according to Pythagoras theorem,
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
⇒ (Hypotenuse)2 = (12)2 + (5)2 ...[∵ Height = Perpendicular]
⇒ (Hypotenuse)2 = 144 + 25
⇒ (Hypotenuse)2 = 169
⇒ Hypotenuse = `sqrt(169)`
⇒ Hypotenuse = 13 cm
APPEARS IN
RELATED QUESTIONS
If A(−4, 8), B(−3, −4), C(0, −5) and D(5, 6) are the vertices of a quadrilateral ABCD, find its area.
Find the area of the triangle whose vertices are: (2, 3), (-1, 0), (2, -4)
Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.
Show that points A(a, b + c), B(b, c + a), C(c, a + b) are collinear.
The four vertices of a quadrilateral are (1, 2), (−5, 6), (7, −4) and (k, −2) taken in order. If the area of the quadrilateral is zero, find the value of k.
In a ΔABC, AB = 15 cm, BC = 13 cm and AC = 14 cm. Find the area of ΔABC and hence its altitude on AC ?
Find the area of ΔABC whose vertices are A(10, –6), B(2, 5) and C(–1, 3).
The coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1 are:
Find the value(s) of k so that the quadratic equation x2 − 4kx + k = 0 has equal roots.
Find the area of the triangle whose vertices are (–8, 4), (–6, 6) and (–3, 9).
