Advertisements
Advertisements
Question
In an isosceles triangle PQR, the length of equal sides PQ and PR is 13 cm and base QR is 10 cm. Find the length of perpendicular bisector drawn from vertex P to side QR.
Advertisements
Solution
Given: In an isosceles triangle PQR, PQ = PR = 13 cm and base QR = 10 cm.
Since, PS is the perpendicular bisector,
∴ QS = SR = `(QR)/2 = 10/2` = 5
Now, using Pythagoras' theorem, in a right-angled triangle PSQ,
PS2 + SQ2 = PQ2
Substituting the values of SQ and PQ in equation (i),
PS2 + 52 = 132
⇒ PS2 = 132 – 52
⇒ PS2 = 169 – 25
⇒ PS2 = 144
∴ PS = `sqrt(144)` = 12
As a result, the length of the perpendicular bisector PS is 12 cm.
APPEARS IN
RELATED QUESTIONS
The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right traingle ,right-angled at B. Find the values of p.
In a ∆ABC, AD ⊥ BC and AD2 = BC × CD. Prove ∆ABC is a right triangle
Sides of triangle are given below. Determine it is a right triangle or not? In case of a right triangle, write the length of its hypotenuse. 13 cm, 12 cm, 5 cm
In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC2 = AB2 + BC2 − 2BC.BD.
ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC.
In ∆ABC, AB = 10, AC = 7, BC = 9, then find the length of the median drawn from point C to side AB.
The given figure shows a quadrilateral ABCD in which AD = 13 cm, DC = 12 cm, BC = 3 cm and ∠ABD = ∠BCD = 90o. Calculate the length of AB.
Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m;
find the distance between their tips.
In the figure, given below, AD ⊥ BC.
Prove that: c2 = a2 + b2 - 2ax.
Diagonals of rhombus ABCD intersect each other at point O.
Prove that: OA2 + OC2 = 2AD2 - `"BD"^2/2`
Find the side of the square whose diagonal is `16sqrt(2)` cm.
The sides of a certain triangle is given below. Find, which of them is right-triangle
6 m, 9 m, and 13 m
In the right-angled ∆LMN, ∠M = 90°. If l(LM) = 12 cm and l(LN) = 20 cm, find the length of seg MN.
Two poles of height 9m and 14m stand on a plane ground. If the distance between their 12m, find the distance between their tops.
From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF2 + BD2 + CE2 = AE2 + CD2 + BF2
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 = AD2 + BC x DE + `(1)/(4)"BC"^2`
In a right-angled triangle PQR, right-angled at Q, S and T are points on PQ and QR respectively such as PT = SR = 13 cm, QT = 5 cm and PS = TR. Find the length of PQ and PS.
Two trees 7 m and 4 m high stand upright on a ground. If their bases (roots) are 4 m apart, then the distance between their tops is ______.
A right-angled triangle may have all sides equal.
