Advertisements
Advertisements
प्रश्न
The sides of certain triangles are given below. Determine which of them right triangles are.
(a – 1) cm, `2sqrta` cm, (a + 1) cm
उत्तर
P = (a-1) cm, q = `2sqrta` 𝑐𝑚 𝑎𝑛𝑑 𝑟=(𝑎+1)𝑐𝑚
Then,
`p^2+q^2=(0a-1)^2+(2sqrta)^2`
=`a^2+1-2a+4a`
=`a^2+1+2a`
=`(a+1)^2`
`r^2=(a+1)^2`
`p^2+q^2=r^2`
Thus, the given triangle is right-angled.
APPEARS IN
संबंधित प्रश्न
State which pair of triangles in the following figure are similar. Write the similarity criterion used by you for answering the question, and also write the pairs of similar triangles in the symbolic form:
In the following figure, `("QR")/("QS") = ("QT")/("PR")` and ∠1 = ∠2. Show that ΔPQS ~ ΔTQR.
S and T are point on sides PR and QR of ΔPQR such that ∠P = ∠RTS. Show that ΔRPQ ∼ ΔRTS.
In the following figure, ABC and AMP are two right triangles, right-angled at B and M respectively, prove that:
- ΔABC ~ ΔAMP
- `("CA")/("PA") = ("BC")/("MP")`
In the given figure, two chords AB and CD intersect each other at the point P. prove that:
(i) ΔAPC ∼ ΔDPB
(ii) AP.BP = CP.DP
In the following Figure, ∠ABC = 90° and BD ⊥ AC. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find BC.
The sides of certain triangles are given below. Determine which of them right triangles are.
7cm, 24cm, 25cm
The corresponding sides of two similar triangles are in the ratio 2 : 3. If the area of the smaller triangle is 48 cm2, find the area of the larger triangle.
If ΔABC ~ ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true?
In figure, if DE || BC, find the ratio of ar(ADE) and ar(DECB).
