Advertisements
Advertisements
Question
In the following figure, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is ______.
Options
6 cm
9 cm
4 cm
2 cm
Advertisements
Solution
In the following figure, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is 4 cm.
Explanation:
Given that, PR = 12 cm, QR = 6 cm and PL = 8 cm
Now, In right angled ΔPLR, using Pythagoras theorem,
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
⇒ PR2 = PL2 + LR2
⇒ LR2 = PR2 – PL2 = (12)2 – (8)2
⇒ LR2 = 144 – 64 = 80
⇒ LR = `sqrt(80) = 4sqrt(5)` cm
∵ LR = LQ + QR
⇒ LQ = LR – QR = `(4sqrt(5) - 6)` cm
Now, area of ΔPLR,
`A_1 = 1/2 xx LR xx PL`
= `1/2 xx (4sqrt(5)) xx 8`
= `16sqrt(5)` cm2
Again, area of ΔPLQ,
`A_2 = 1/2 xx LQ xx PL`
= `1/2 xx (4sqrt(5) - 6) xx 8`
= `(16sqrt(5) - 24)` cm2
∴ Area of ΔPLR = Area of ΔPLQ + Area of ΔPQR
⇒ `16sqrt(5) = (16sqrt(5) - 24)` + Area of ΔPQR
⇒ Area of ΔPQR = 24 cm2
⇒ `1/2 xx PR xx QM = 24`
⇒ `1/2 xx 12 xx QM = 24`
∴ QM = 4 cm
APPEARS IN
RELATED QUESTIONS
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.
Prove that the points (2a, 4a), (2a, 6a) and `(2a + sqrt3a, 5a)` are the vertices of an equilateral triangle.
A(6,1) , B(8,2) and C(9,4) are the vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of ΔADE
For what value of y, are the points P(1, 4), Q(3,y) and R(-3, 16) are collinear ?
Prove that the points A (a,0), B( 0,b) and C (1,1) are collinear, if `( 1/a+1/b) =1`.
In Figure 1, PS = 3 cm, QS = 4 cm, ∠PRQ = θ, ∠PSQ = 90°, PQ ⊥ RQ and RQ = 9 cm. Evaluate tan θ.
The table given below contains some measures of the right angled triangle. Find the unknown values.
| Base | Height | Area |
| 5 feet | ? | 20 sq.feet |
Points A(–6, 10), B(–4, 6) and C(3, –8) are collinear such that AB = `2/9` AC.
Observe all the four triangles FAB, EAB, DAB and CAB as shown in the following figure.
- All triangles have the same base and the same altitude.
- All triangles are congruent.
- All triangles are equal in area.
- All triangles may not have the same perimeter.
If (a, b), (c, d) and (e, f) are the vertices of ΔABC and Δ denotes the area of ΔABC, then `|(a, c, e),(b, d, f),(1, 1, 1)|^2` is equal to ______.
